ECE 8527 Homework Final: Common Evaluations By Andrew Powell

Outline Introduction Objectives Tools Obstacles Algorithms (Training / Classification / Performance) Hidden Markov Models (HMM) K-Nearest Neighbors (KNN) Neural Network (NN) Conclusion Final Thoughts References

Outline Introduction Objectives Tools Obstacles Algorithms (Training / Classification / Performance) Hidden Markov Models (HMM) K-Nearest Neighbors (KNN) Neural Network (NN) Conclusion Final Thoughts References

Introduction: Objectives Select three nontrivial, machine-learning algorithms supported in MATLAB ©. The selected algorithms are the following. Hidden Markov Models (HMM) *** K-Nearest Neighbors (KNN) Neural Networks (NN) Determine the performance of the selected algorithms as a function of their “key” parameters through a series of simulations. Recognition Error Rate Discriminant Values Timing Analysis Present the information.

Introduction: Tools MATLAB Used for all the programming and simulation Important to note since performing the same simulations in different languages/environments will most likely produce different results Kevin Murphy’s Hidden Markov Model Toolbox Used for training HMMs that emit Gaussian-mixtures and classification HMM training supported in MATLAB’s Statistics Toolbox is relatively more difficult to use since there is no built-in support for continuous observations. Statistics Toolbox Used for classification with KNN Neural Network Toolbox Used for training regular feed-forward NN and classification

Introduction: Obstacles Timing Although determining the time it takes to train the models and classify the data vectors is relatively simple, comparing the timing results of each algorithm with each other’s timing results is problematic since a number of factors impact how well an algorithm can perform. The focus will be on how the timing results change when parameters are altered Discriminant Values Part of the project requires to show that the recognition error rates correlate with the discriminant values generated for the purpose of classifying the data vectors. Due to the nature of how MATLAB’s proprietary toolboxes are implemented (e.g. Statistics Toolbox), it is difficult to obtain these values with the functions that perform the classification.

Outline Introduction Objectives Tools Obstacles Algorithms (Training / Classification / Performance) Hidden Markov Models (HMM) K-Nearest Neighbors (KNN) Neural Network (NN) Conclusion Final Thoughts References

Algorithms: Hidden Markov Models Introduction A HMM model is created for each class. Each model consists of transitional probabilities from one hidden state to another and the Gaussian mixtures emitted from each hidden state. Training of each model is of course done with the Baum-Welch (i.e. Expectation Maximization) algorithm. Prior to training, the models are randomized but stochastic matrices are ensured. The sequential data vectors of each class are considered to result from sequential time steps, and a class’s entire set of data vectors is interpreted as a single set of data Classification of a data vector is simply choosing the class whose model produces the largest log-likelihood. Parameters Iterations of Trainingdomain: 1 to 4, inclusively Number of Mixturesdomain: 1 to 4, inclusively Number of Hidden Statesdomain: 1 to 10, inclusively Performance Metrics Recognition Error Rate Average Difference between Largest and Second-Largest Log-Posterior Training Time Classification Time

Algorithms: Hidden Markov Models

Key Observations Recognition error rate is relatively low for fewer iterations The average difference between the two largest discriminant values for each assignment correlates with the recognition error rate, excluding when the number of hidden states is equal to 1. The more iterations appears to cause to the recognition error rate to increase.

Algorithms: K-Nearest Neighbors Introduction Computation is all done during classification Classification of a data vector is simply determining closest neighboring data vectors and then selecting the class that has the most data vectors within the set of closest neighboring data vectors. Parameters Number of Neighborsdomain: odd numbers between 1 to 201, inclusively Performance Metrics Recognition Error Rate Classification Time

Algorithms: K-Nearest Neighbors

Key Observations The recognition error rate actually grows with larger number of neighbors (i.e. k)

Algorithms: Neural Networks Introduction The single output of the forward-feed NN is converted from a continuous value to one of the possible discrete values (i.e. the possible classes) with Nearest Neighbors (i.e. KNN, where K=1). The training algorithm for the weights and biases is simply MATLAB’s default algorithm: Levenberg-Marquardt Recommended by MATLAB for its speed, though requires more memory The Neural Network Training toolbox allows for the manipulation of many parameters (such as allowing parallelization over GPUs and cross-validation); however, to keep the simulations relatively simple, only two parameters are modified Parameters Number of Layersdomain: 1, 5, 10, and 15 Number of Neutrons Per Layerdomain: 1, 5, 10, and 15 Performance Metrics Recognition Error Rate Average Distance from Selected Class Training Time Classification Time

Algorithms: Neural Networks

Key Observations In regards to classification, extra neutrons per layer do not appear to have much of an affect on the classification time. Extra layers appear to increase the classification time linearly. In regards to training, extra layers and neutrons per layer greatly increase training time.

Outline Introduction Objectives Tools Obstacles Algorithms (Training / Classification / Performance) Hidden Markov Models (HMM) K-Nearest Neighbors (KNN) Neural Network (NN) Conclusion Final Thoughts References

Conclusion: Final Thoughts Simulations for the algorithms HMM, KNN, and NN were implemented. The algorithms were tested for their performance Recognition Error Rate Discriminant Values Timing Analysis

Conclusion: References Keven Murphy’s HMM Implementation: Neural Network Toolbox and Statistics Toolbox MATLAB documentation